Re: Add Applicative instances for MTL types

On Wed, Jan 14, 2009 at 12:16 PM, Bas van Dijk wrote:

On Wed, Jan 14, 2009 at 2:50 PM, Ross Paterson wrote:

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Even though Applicative is not a superclass of Monad, I think we ought to ensure that the instances are compatible. That is, if an Applicative is also a Monad, then we should have pure = return and (<*>) = ap.

Yes, but what if an Applicative isn't a Monad?

We can't have two instances because they overlap:

instance Monad m => Applicative (ErrorT e m) where pure = return (<*>) = ap

instance Applicative m => Applicative (ErrorT e m) where pure = ErrorT . pure . pure ef <*> ex = ErrorT $ liftA2 (<*>) (runErrorT ef) (runErrorT ex)

I think the latter is more useful because there are more Applicatives than Monads out there.

The latter is just normal composition of applicative functors, in this case "Comp m (Either e)". newtype Comp f g x = Comp { unComp :: f (g x) } instance (Functor f, Functor g) => Functor (Comp f g) where fmap f = Comp . fmap (fmap f) . unComp instance (Applicative f, Applicative g) => Applicative (Comp f g) where pure = Comp . pure . pure f <*> x = Comp $ liftA2 (<*>) (unComp f) (unComp x) Given how easy it is to combine different functors and applicative functors, there isn't very much need for (applicative) functor transformers. I agree with Ross, the functor and applicative instances for monad transformers should satisfy these laws: fmap = liftM pure = return (<*>) = ap

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This fails for your ErrorT instance: ap runs the second computation only if the first succeeded, while (<*>) runs them both before checking for errors. It needs a Monad constraint (like StateT), though not an Error constraint.

But isn't 'runErrorT ex' only evaluated when 'runErrorT ef' returns 'Right f' because of lazy evaluation?

No, in your definition, the effects of the transformed applicative functor are evaluated regardless of the error condition. Try this code: runState (runErrorT (throwError "!" <*> put False)) True The first definition of <*> returns (Left "!", True). The second returns (Left "!", False). -- Dave Menendez http://www.eyrie.org/~zednenem/